Duality of string amplitudes in a curved background

TL;DR

This paper explores the duality of string amplitudes in a curved SU(2) background, demonstrating equivalence with quantum field theory amplitudes and analyzing their relationship in such curved spaces.

Contribution

It introduces a framework to compare string and quantum field theory amplitudes on curved backgrounds, focusing on the SU(2) manifold and duality between channels.

Findings

Established equivalence between string and quantum field theory amplitudes in a curved background.

Derived the general form of a four-scalar field theory amplitude.

Performed a specific string theory amplitude calculation for the SU(2) case.

Abstract

We initiate a program to study the relationship between the target space, the spectrum and the scattering amplitudes in string theory. We consider scattering amplitudes following from string theory and quantum field theory on a curved target space, which is taken to be the $SU(2)$ group manifold, with special attention given to the duality between contributions from different channels. We give a simple example of the equivalence between amplitudes coming from string theory and quantum field theory, and compute the general form of a four-scalar field theoretical amplitude. The corresponding string theory calculation is performed for a special case, and we discuss how more general string theory amplitudes could be evaluated.